You are viewing a javascript disabled version of the site. Please enable Javascript for this site to function properly.
Go to headerGo to navigationGo to searchGo to contentsGo to footer
In content section. Select this link to jump to navigation

Splitting and matrix exponential approach for jump-diffusion models with Inverse Normal Gaussian, Hyperbolic and Meixner jumps

Abstract

This paper is a further extension of the method proposed in Itkin (2014) as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the diffusion equation we use standard finite-difference methods. For the jump part, we transform the jump integral into a pseudo-differential operator and construct its second order approximation on a grid which supersets the grid used for the diffusion part. The proposed schemes are unconditionally stable in time and preserve positivity of the solution which is computed either via a matrix exponential, or via its Páde approximation. Various numerical experiments are provided to justify these results.